## frank0520 one year ago Let F be the vector field F=(13x^2 y+3y^3 -y)i -12x^3 j. Find the maximum value of ∫F•dr where c is positively oriented simple closed curve.

1. ganeshie8

2. ganeshie8

@dan815

3. ganeshie8

$\oint F.dr = \iint\limits_{R} \text{curl}(F)~dA = \iint\limits_{R} -49x^2-9y^2+1~dA$

4. ganeshie8

Easy to see that the integrand stays positive in the region $$49x^2+9y^2 \lt 1$$, so should we pick this as region of integration ?

5. frank0520

Here is a picture of the question.

6. ganeshie8

Then we're correct, go ahead and evaluate the integral over that ellipse

7. ganeshie8

$max(\oint F.dr) ~= ~\iint\limits_{49x^2+9y^2\lt 1}~~1-49x^2-9y^2~dA$

8. ganeshie8

you will need to use change of variables

9. ganeshie8

I'm getting $$\dfrac{21\pi}{2}$$ http://www.wolframalpha.com/input/?i=21*%5Cint_0%5E%282pi%29%5Cint_0%5E1+%281-r%5E2%29*r+dr+d%5Ctheta

10. frank0520

looks correct to me, I got $\frac{ 42\pi }{ 4 }$